An algebraic geometric model of an action of the face monoid associated to a Kac-Moody group on its building

作者：Mokler C^*

来源：Journal of Pure and Applied Algebra, 2015, 219(2): 331-397.

DOI：10.1016/j.jpaa.2014.04.024

The face monoid (G) over cap described in [11] acts on the integrable irreducible highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a symmetrizable Kac-Moody group G. We found in [15] two natural extensions of the action of the Kac-Moody group Con its building Omega to actions of the face monoid (G) over cap on the building Omega. Now we give an algebraic geometric model of one of these actions of the face monoid (G) over cap on Omega, where the building Omega is obtained as a part of the IF-valued points of the spectrum of all homogeneous prime ideals of the Cartan algebra CA of the Kac-Moody group G. We describe the spectrum of all homogeneous prime ideals of the Cartan algebra CA and determine its F-valued points.

• 出版日期2015-2